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Orthogonal Polynomials of Several Variables
 Encyclopedia of Mathematics and its Applications
, 2001
"... Abstract. We report on the recent development on the general theory of orthogonal polynomials in several variables, in which results parallel to the theory of orthogonal polynomials in one variable are established using a vectormatrix notation. 1 ..."
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Cited by 235 (44 self)
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Abstract. We report on the recent development on the general theory of orthogonal polynomials in several variables, in which results parallel to the theory of orthogonal polynomials in one variable are established using a vectormatrix notation. 1
U * VECTOR/MATRIX GUANTIZA TION FOR NARROWBANDWIDTH DIGITAL SPEECH COMPRESSION
, 1982
"... smmhhmhhmmhiu smhhhhhhhhmhl smhhhhhshEEEE 7E ND oos ..."
A linearly convergent dualbased gradient projection algorithm for quadratically constrained convex minimization
 Mathematics of Operations Research
, 2006
"... Abstract. This paper presents a new dual formulation for quadratically constrained convex programs (QCCP). The special structure of the derived dual problem allows to apply the gradient projection algorithm to produce a simple explicit method involving only elementary vectormatrix operations, that ..."
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Cited by 2 (0 self)
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Abstract. This paper presents a new dual formulation for quadratically constrained convex programs (QCCP). The special structure of the derived dual problem allows to apply the gradient projection algorithm to produce a simple explicit method involving only elementary vectormatrix operations
An Overview of Multichannel Image Restoration Techniques
 in Week of Doctoral Students
, 1999
"... In this paper we provide a general overview of multichannel (MC) restoration techniques. We do not give a detailed description of individual methods but rather provide a classification of MC techniques. We present a general MC degradation model in a vectormatrix notation and we state some useful pr ..."
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Cited by 2 (0 self)
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In this paper we provide a general overview of multichannel (MC) restoration techniques. We do not give a detailed description of individual methods but rather provide a classification of MC techniques. We present a general MC degradation model in a vectormatrix notation and we state some useful
Cache efficient bidiagonalization using BLAS 2.5 operators
, 2003
"... On cache based computer architectures using current standard algorithms, Householder bidiagonalization requires a significant portion of the execution time for computing matrix singular values and vectors. In this paper we reorganize the sequence of operations for Householder bidiagonalization of a ..."
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Cited by 16 (1 self)
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general m × n matrix, so that two ( GEMV) vectormatrix multiplications can be done with one pass of the unreduced trailing part of the matrix through cache. Two new BLAS 2.5 operations approximately cut in half the transfer of data from main memory to cache. We give detailed algorithm descriptions
Optimal Registration of Object Views Using Range Data
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1997
"... This paper deals with robust registration of object views in the presence of uncertainties and noise in depth data. Errors in registration of multiple views of a 3D object severely affect view integration during automatic construction of object models. We derive a minimum variance estimator (MVE) fo ..."
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Cited by 61 (0 self)
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This paper deals with robust registration of object views in the presence of uncertainties and noise in depth data. Errors in registration of multiple views of a 3D object severely affect view integration during automatic construction of object models. We derive a minimum variance estimator (MVE) for computing the view transformation parameters accurately from range data of two views of a 3D object. The results of our experiments show that view transformation estimates obtained using MVE are significantly more accurate than those computed with an unweighted error criterion for registration. Key words: Image registration, view transformation estimation, view integration, automatic object modeling, 3D freeform objects, range data. 1 Introduction An important issue in the design of 3D object recognition systems is building models of physical objects. Object models are extensively used for synthesizing and predicting object appearances from desired viewpoints and also for recognizing th...
Incremental spectral clustering with application to monitoring of evolving blog communities
 In SDM
, 2007
"... In recent years, spectral clustering method has gained attentions because of its superior performance compared to other traditional clustering algorithms such as Kmeans algorithm. The existing spectral clustering algorithms are all offline algorithms, i.e., they can not incrementally update the cl ..."
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Cited by 27 (5 self)
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to handle not only insertion/deletion of data points but also similarity changes between existing items. This paper extends the standard spectral clustering to such evolving data by introducing the incidence vector/matrix to represent two kinds of dynamics in the same framework and by incrementally updating
Lines in Space—Part 3: The Two Matrices
 IEEE Computer Graphics and Applications
"... In our last episode, we came up with two algebraic representations for lines in 3D projective space: we got one from connecting two points and the other from intersecting two planes. In both cases the algebraic representation was an antisymmetric 4 × 4 matrix, but these two matrices were not the sam ..."
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Cited by 3 (3 self)
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what I call conventional, or familiar, notation. This gives letter names to each element of a vector/matrix and, I think, gives a sense of concreteness to the calculations. In this sense, it will be a recapitulation of my 1977 Siggraph paper1 on this subject. But I’ll get in a few subtle digs
CSL model checking of biochemical networks with interval decision diagrams
 in Proc. CMSB 2009. LNCS/LNBI 5688
, 2009
"... Abstract. This paper presents an Interval Decision Diagram based approach to symbolic CSL model checking of Continuous Time Markov Chains which are derived from stochastic Petri nets. Matrixvector and vectormatrix multiplication are the major tasks of exact analysis. We introduce a simple, but po ..."
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Cited by 12 (7 self)
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Abstract. This paper presents an Interval Decision Diagram based approach to symbolic CSL model checking of Continuous Time Markov Chains which are derived from stochastic Petri nets. Matrixvector and vectormatrix multiplication are the major tasks of exact analysis. We introduce a simple
Panoramic Image Mosaics
, 1997
"... This paper presents some techniques for constructing panoramic image mosaics from sequences of images. Our mosaic representation associates a transformation matrix with each input image, rather than explicitly projecting all of the images onto a common surface (e.g., a cylinder). In particular, to c ..."
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Cited by 58 (5 self)
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This paper presents some techniques for constructing panoramic image mosaics from sequences of images. Our mosaic representation associates a transformation matrix with each input image, rather than explicitly projecting all of the images onto a common surface (e.g., a cylinder). In particular, to construct a full view panorama, we introduce a rotational mosaic representation that associates a rotation matrix (and optionally a focal length) with each input image. A patchbased alignment algorithm is developed to quickly align two images given motion models. Techniques for estimating and refining camera focal lengths are also presented. In order to reduce accumulated registration errors, we apply global alignment (block adjustment) to the whole sequence of images, which results in an optimally registered image mosaic. To compensate for small amounts of motion parallax introduced by translations of the camera and other unmodeled distortions, we develop a local alignment (deghosting) tec...
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